Optimizing search through large list of lat/long coords to find match

Question

I need to create a page that

1. takes 2 addresses (to and from),
2. plots the route AND areas within 1 mile of this route,
3. THEN figure out if any of a predefined list of thousands of lat/long coords falls within this area (w/ 1 mile, along the route)

I'm using google-maps v3 api and the routeboxer class.
Here is a good example: http://google-maps-utility-library-v3.googlecode.com/svn/trunk/routeboxer/examples/routeboxer-v3.html
As you can see, #1 and #2 are basically taken care of by this routeboxer example.

My question is about handling #3 EFFICIENTLY. Routeboxer provides a series of box-coords (North East lat/long to South West lat/long corners). I can loop box by box and then loop within each of the predefined lat/long coords to see if any coord in the list falls within the area of the routeBoxes, but this is a lengthy, inefficient process.

I am looking for a means to optimize this (#3) search portion. Some ideas:

1. a binary search; would require sorting the coord list by lat, then long - but would likely speed things up
2. mySQL query: this takes processing off the usersPC and puts it onto our servers; I would query for each routeBox:
   select * from myListOfLatLongs where lat box_latwest && lng box)lngsouth

Which is more ideal for speed & stability? Are there any better ideas/opimizations? The bottom line is that without optimization, this can theoretically return MANY boxes, and each box would then need to be compared against thousands of coords -- which can become a lengthy process. Any help appreciated

Answer 1

Subdivide your lat/long space into cells of some appropriate size, and sort the locations into those cells.

Then, for each point along your route, do a spiral search outward among the cells to find the nearest neighbors.

P.S. Spiral search. You can do it on squares, bricks, or hexagons like this. If the tiles are big enough to contain some points but not too many, if finds neighbors quickly.

Just transform the latitude and longitude into the above coordinate system, round them to the nearest center, and make a bucket for each cell. Then take your search point and find its bucket. If nothing useful is found in its bucket, search the six buckets at radius 1, and so on, until a suitable collection of neighbors is found, and pick the best one. The sequence of cells looks like this, assuming 0,0 is the starting cell:

look in 0,0
++x

++y
--x
--x,--y
--y
++x
++y,x+=2

++y twice
--x twice
--x,--y twice
--y twice
++x twice
++x,++y
++y,x+=2

etc. etc.

EDIT: some C++ code to do it

// for each point x,y, do this (d is diameter of a cell)
double x1 = (x + y/2)/d;  // transform x coordinate
double y1 = (y / 0.866)/d;  // transform y coordinate (it's shortened a bit)
int ix = (int)floor(x1 + 0.5);  // find corresponding bucket
int iy = (int)floor(y1 + 0.5);
// then put point into bucket at ix,iy

// to search, enumerate over the cells
// first at distance 0, then 1, then 2, etc.
bool bPointsFound = false;
// collect points in bucket at 0,0
if (/* there are any points in the collection */){
  bPointsFound = true;
}
for (n = 1; n < upper_limit && !bPointsFound; n++){
  iy = 0; ix = n;
  // upper right edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    iy++;
  }
  // top edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    ix--;
  }
  // upper left edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    ix--; iy--;
  }
  // lower left edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    iy--;
  }
  // bottom edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    ix++;
  }
  // lower right edge
  for (i = 0; i < n; i++){
    // collect points in bucket at ix, iy
    ix++; iy++;
  }
  if (/* there are any points in the collection */){
    bPointsFound = true;
  }
}
// pick the closest point in the collection

ADDED: There is a slight possibility of getting a point which is not the closest, because a point just outside the edge of a hexagon might be closer than a point just inside the corner. If that's a concern, go out to an extra layer.

Answer 2

You can use a spatial index and search for a 2d range,i.e. bounding box. For example with the MySQL spatial extension. You can also try my hilbert curve class (phpclasses.org) it uses a quadkey with a range search and it's a pure php solution. You can also try a quadtree it has some better perfomance over a r-tree.